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Chemical Engineering 374
Fluid Mechanics
Lecture 2
Fluid Properties
Spiritual Thought
• D&C 42:2
“If thou shalt ask, thou shalt receive
revelation upon revelation, knowledge upon
knowledge, that thou mayest know the mysteries
and peacable things – that which bringeth joy, that
which bringeth life eternal”
• D&C 46:18
“ To another is given the word of knowledge,
that all may be taught to be wise and to have
knowledge.”
2
Fluids Roadmap3
Key Points
• Fluid Definition
– Sheer Stress
• Fluid Properties
1. Density
• Density variation with P,T
2. Viscosity (molecular interpretation, equation)
• Temperature/pressure effect on viscosity
• Newtonian fluids
• Non-Newtonian fluids
3. Kinematic Viscosity
4
What is a Fluid?
– Liquid or Gas
– “deforms continuously under applied shear
stress”
– Liquid: form a free surface
– Gases: fill volume, no free surface, mixing
5
Fluid?6
Continuum vs. Particles7
Mass
Length (nm scale)
Distinct Particles
Length (m scale)
Mass
Continuum
Density
• mass/volume
– metric vs. British?» 1000 kg/m3, 1.2 kg/m3
» 62.3 lbm/ft3, 0.0752 lbm/ft3
• Specific Gravity
• Specific Weight
• Industry Specific
– Degrees API, Brix Gravity, Degrees Baume, etc.
8
Density9
0
2000
4000
6000
8000
10000
12000
14000
16000
Mercury Water Seawater SAE 30 oil Gasoline
De
nsit
y (k
g/m
3)
0
200
400
600
800
1000
1200
Water Seawater SAE 30 oil Gasoline
De
nsit
y (
kg
/m3)
Density Changes
• Gas: Ideal Gas
• Liquid: nearly constant
– 4% variation in T 0 ˚C to 100 ˚C
– 1% variation in P 1 atm to 200 atm
10
Density of water versus temperature
Fundamentals of Fluid Mechanics, 5/E by Bruce Munson, Donald Young, and Theodore Okiishi
Copyright © 2005 by John Wiley & Sons, Inc. All rights reserved.
4%
variation
Density changes w/ Pressure12
• Coefficient of Compressibility
Density changes w/ Temperature13
• Coefficient of Volume Expansion
Examples14
Harry potter, when transmuting a tank of water (3m3 at 1 atm) accidentally
shrinks the walls of the tank (while not changing the mass of water inside) to 2
m3. How much additional pressure is exerted on the walls of the tank as a
result? (κ = 21,000 atm)
On his next attempt he uses less water (only 1 m3) in the same tank, but he
increases the temperature by 300 ˚C. How much volume does the water now
take up? (β = 2.61x10-4/K)
Viscosity15
Viscosity I16
Viscosity II17
Viscosity Changes with T & P18
• Liquids: molecules are everywhere,
constantly getting in way of motion
– T up, molecules move faster…
• μ decreases
• gases: molecules are sparce, rarely hit
each other
– T up, molecules move faster…
• more frequent collisions, μ increases
• Pressure:
– Small effect for both
Kinematic Viscosity19
• ν (units of m2/s)
• Μ steam vs. water is factor 100 different
• Ρ sream vs. water is Factor 1000 different
Non-Newtonian Fluids20
m
dv/dy
m
dv/dy
m
dv/dy
m
dv/dy
t
dv/dy
t
dv/dy
t
dv/dy
t
dv/dy
Newtonian Bingham Plastic Pseudoplastic Dilitant
t=m*dv/dy t=m*dv/dy + ty t=k*|dv/dy|n